Final answer:
To solve the linear equation 4(2z+7)-30=2(-3z+6), distribute and simplify both sides of the equation, combine like terms, isolate z on one side of the equation, and divide by the coefficient of z.
Step-by-step explanation:
To solve the linear equation 4(2z+7)-30=2(-3z+6), we will start by distributing and simplifying both sides of the equation:
First, distribute: 8z + 28 - 30 = -6z + 12
Combine like terms: 8z - 2 = -6z + 12
Add 6z to both sides: 14z - 2 = 12
Add 2 to both sides: 14z = 14
Finally, divide by 14 to solve for z: z = 1